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As summer draws to a close and the city’s school doors are set to open, a parents group has asked the city’s mayoral candidates to endorse their new proposal: a lottery for every public school.

The group is called Families for Excellent Schools and has a history of supporting reform efforts such as opening more charters. But this latest is a novel idea.

The group is asking that the next mayor permit a lottery system for all public schools, add more seats to quality academic programs — and continue giving charter schools available free space in public schools. In other words, it challenges the public schools to live up to the promise to give every child in New York an equal shot at a good education.

Charter schools already use lotteries to pick students. They’ve found it the fairest way to distribute the limited supply of charter seats in the face of a demand that this year left 50,000 kids disappointed.

But imagine what might happen if there are lotteries for all public schools. Kids trapped in failing schools with no chance at charters would overnight have far more options.

Meanwhile, wealthy parents who solved their public-school problem by moving into a better neighborhood might have an interest in ensuring that there was more choice for all parents if they weren’t so certain their own children could get into the well-off public school around the corner. It doesn’t get more egalitarian than this.

In short, a system-wide lottery might unite parents of all economic backgrounds to demand reform. We’re doubtful there’s going to be many candidates willing to embrace this measure. But we’d sure like to hear them explain publicly why not.